比利时vs摩洛哥足彩
,
university of california san diego
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representation theory
hanspeter kraft
university of basel, switzerland
equations for field extensions and covariants of the symmetric
abstract:
for a given finite separable field extension $l/k$ we would like to find a generator $x \in l$ whose equation is as simple as possible. for example, one would like to have as many vanishing coefficients as possible. more generally, the transcendence degree of the subfield $k$ of $k$ generated by the coefficients of the equation should be as small as possible. it was shown by buhler and reichstein that the minimal transcendence degree one can reach has an interpretation in terms of rational covariants of the symmetric group $s_n$ where $n := [l:k]$. this number is called the essential dimension of $l/k$ or of $s_n$ it can be defined for every finite group. we will describe the relation between covariants and equations for field extensions and will explain the main results in this context.
host: k. baur
september 28, 2004
2:00 pm
ap&m 7321
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